Guiding-center-drift resonance in a periodically modulated two-dimensional electron gas

Spatially modulated semiconductor structures in a magnetic field have unusual properties due to the interplay of the two independent periodicities of the modulation and the cyclotron orbit. Recently, Weiss, von Klitzing, Ploog, and Weimann' discovered a striking manifestation of this interplay in the magnetoresistance of a two-dimensional electron gas (2DEG) subject to a weak periodic potential Variation in one direction (a potential grating). At low magnetic fields B (perpendicular to the 2DEG) an oscillation periodic in l/B was observed in the resistance, reminiscent of the Shubnikov-de Haas (SdH) oscillations at higher fields—but with a different periodicity and a much weaker temperature dependence. The new periodicity was found to be given by the condition that the cyclotron orbit radius R=mvp/eB is an integer multiple for the modulation period a (VF is the Fermi velocity). Weiss et al. remarked that this periodicity corresponds to SdH oscillations where only electrons within the first Brillouin zone of the modulated structure contribute, but no mechanism was found to support an explanation along these lines. Theoretically, the transport properties of a periodically modulated 2DEG have been studied with the emphasis on effects originating from the band structure of the lateral superlattice. In the experiments of Weiss et al., however, the period a—0.3-0.4 μτα is considerably larger than the Fermi wavelength λρ=2π^ρ~50 nm, suggesting a different origin of their effect. Moreover, the weak temperature dependence of the oscillation amplitude indicates that magnetic quantization in Landau levels (responsible for the SdH oscillations) does not play an important role. These considerations motivated me to look for a semiclassical explanation. I have found that the magnetoresistance oscillation induced by a potential grating is due to a resonance in the Ex B drift of the cyclotron orbit (guiding) center. Such resonances are known from plasma physics,· and the experiment by Weiss et al. appears to be the first observation of this phenomenon in the solid state. This paper consists of two parts. A detailed systematic transport theory is developed, based on the semiclassical Boltzmann equation in the relaxation-time approximation. The analysis is somewhat involved because of the presence of both a magnetic field and an inhomogeneous electric field. Therefore, I first present a simplified physical picture of the resonance mechanism and its effect on the transport properties. The guiding center (X, Y) of an electron at position (x,y) having velocity (f*,^) is given by X—x — vy/(ac, Y—y + vx/(ox, with

ReadCiteExport

Add to List

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Sign up to Zendy

Having issues? You can contact us here